We recently visited all 5 Utah National Parks in 5 days with 5 kids! When going at this kind of pace you really have to be picky about what hikes you choose. So here is our choice for the best hike at Bryce Canyon National Park:
Navajo Loop/Queens Garden trail.
This hike can either be done as a loop combining the Navajo Trail and Queens Garden Loop, or it can be done as two separate out-and-back hikes. I highly recommend the combination loop, to avoid doing the steep switchbacks more than necessary!
The loop hike can begin at Sunset point and starts with a long series of switchbacks. Then it evens out and become a mostly flat dirt trail. You encounter gorgeous hoodoos and towering fir trees all along the route. Follow this until you reach the signs for the Queens Garden trail.
After walking around the Queens Garden section, you return to the trail and start the ascent to the parking lot. The trail gets a little confusing so make sure you pass through the tiny walkway (see the picture below) as you exit the Queens Garden toward Sunrise point.
Don’t miss this turn! 
Switchbacks to the exit 
Basics of the Navajo trail/Garden Loop trail!
600 feet of elevation gain (this hike starts with some major downhill and ends with major uphill)
2.9 mile moderately strenuous loop (Start from either Sunrise or Sunset point)
Parking area has bathroom facilities, water fountains, and the parking lots fills quickly!
This is kid friendly. Just beware of some steep drop offs. My 5 and 8 year old hiked it without too much difficulty.
https://www.nps.gov/brca/index.htm
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